A car with an initial velocity of 8 m/s experiences a constant acceleration for 3 sec, after which the velocity is 17 m/s.
a) What was the acceleration?
b) How far did the car travel during that time interval?
What would the equations be for each of these questions?
To determine the acceleration and distance traveled by the car, we can use the equations of motion, specifically the formulae related to acceleration, initial velocity, time, and displacement.
a) The equation to calculate acceleration is:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time (t)
b) The equation to calculate displacement is:
Displacement (s) = (Initial velocity (u) * Time (t)) + (0.5 * Acceleration (a) * Time (t)^2)
Let's use these equations to find the answers to the given questions.
a) To calculate the acceleration:
Initial velocity (u) = 8 m/s
Final velocity (v) = 17 m/s
Time (t) = 3 seconds
Substituting these values into the formula:
Acceleration (a) = (17 m/s - 8 m/s) / 3 s
= 9 m/s / 3 s
= 3 m/s^2
Therefore, the acceleration of the car is 3 m/s^2.
b) To calculate the distance traveled during the time interval:
Initial velocity (u) = 8 m/s
Time (t) = 3 seconds
Acceleration (a) = 3 m/s^2
Substituting these values into the formula:
Displacement (s) = (8 m/s * 3 s) + (0.5 * 3 m/s^2 * (3 s)^2)
= 24 m + 0.5 * 3 m/s^2 * 9 s^2
= 24 m + 0.5 * 3 m/s^2 * 81 s^2
= 24 m + 0.5 * 3 m/s^2 * 81 s^2
= 24 m + 0.5 * 3 m/s^2 * 81 s^2
= 24 m + 0.5 * 3 m/s^2 * 81 s^2
= 24 m + 0.5 * 3 m/s^2 * 81 s^2
= 24 m + 121.5 m
= 145.5 m
Therefore, the car traveled a distance of 145.5 meters during the given time interval.